1. Field of the invention
The present invention relates to methods of estimating shear wave velocity and, more particularly, to such methods and related systems for estimating the shear wave velocity of subterranean formation materials of the type where direct measurements of shear wave velocity are unobtainable by conventional methods.
2. Setting of the Invention
Through the years seismic explorationists employed in the search for subterranean hydrocarbons have utilized compressional wave velocities (V.sub.p) to obtain information regarding subterranean features. Recently, shear wave velocities (V.sub.s) have been utilized, along with such compressional wave velocities (V.sub.p), to obtain a better understanding of the earth's subsurface features. One method of obtaining shear wave velocities is commonly referred to as sonic wave train logging, which utilizes sonic frequencies of about 5 to about 50 Kz. A monopole source and receiver array is placed within a fluid-filled wellbore to measure the formation's elastic properties via acoustic-elastic energy mode conversions at the wellbore fluid-formation interface. The sonic or acoustic monopole energy transmitting device generates acoustic compressional waves, which are converted at the borehole wall to both compressional and shear elastic waves critically refracted in the formation.
A problem with obtaining measurements of shear wave velocity often encountered in the field is that the formation to be logged has a shear wave velocity which is less than the acoustic velocity of the fluid within the wellbore. As is well known, in such instances no critically refracted formation shear waves are generated via the acoustic-elastic mode conversion at the wellbore fluid-formation interface; thus, no shear wave can be detected by the receivers. This problem is particularly common in offshore coastal regions, such as the United States Gulf Coast, where unconsolidated formation materials are prevalent.
Various solutions to this important problem have been proposed in the past. One approach has been to place multipole source-receiver acoustic arrays in a wellbore to directly impart and sense shearing motion at the wellbore wall without relying upon acoustic-elastic mode conversion. A problem with using such acoustic arrays is the requirement of azimuthal alignment and centering of the receivers and the transmitters within the wellbore. Another method has been proposed in U.S. Pat. No. 4,754,439, wherein the acoustic velocity of the wellbore fluid is altered in order to obtain shear wave velocity signals. Yet another approach relies upon other modes of borehole acoustic energy propagation, such as the Stoneley or the "tube wave." These waves are generated even when the formation shear velocity is less than the borehole fluid velocity and can be recorded and analyzed to infer formation shear velocity via known theoretical relationships. The analysis procedures used to "back out" the formation shear velocity from the Stoneley or "tube wave" are computationally intensive. One such method is disclosed in U.S. Pat. No. 4,633,449. Further, these computational methods to back out the shear velocity require exceptionally good data quality to yield stable numerical results.
Various research efforts have been directed to establishing alternative, less computationally intensive means for inferring shear wave velocity from other modes of borehole wave propagation, such as the compressional wave. It has been known that formation compressional wave velocity (V.sub.p) and shear wave velocity (V.sub.s) are functions of formation bulk modulus (K), shear modulus (G), and density (.rho.) according to the equations: ##EQU1## Knowing the formation material density (.rho.), such as from a conventional formation density log, the shear modulus (G) and the shear wave velocity (V.sub.s) can be calculated from the compressional wave velocity (V.sub.p) (obtained from a conventional sonic log) if the corresponding value of formation bulk modulus (K) is known, such as from published relationships and other databases. Then the above equations can be rewritten as: EQU 4/3G=.rho..multidot.V.sub.p.sup.2 -K (2)
Hence, the estimation of the formation shear wave velocity (V.sub.s) becomes a matter of determining the appropriate insitu value for the bulk modulus (K) of the formation material.
Biot-Gassmann theory (Gassmann, Geoph., 16, 673, 1951) directs that formation elastic moduli can be expressed in terms of the corresponding dry rock frame moduli plus a correction term which explicitly accounts for the effect of formation pore fluids. The resulting expressions for the bulk modulus (K) and shear modulus (G) thus become: ##EQU2## EQU G=G* (3c)
Wherein the bulk and shear moduli of the porous rock frame work (i.e., the "frame"moduli) are K* and G* respectively, the bulk modulus of the formation pore fluid is K.sub.f, the aggregate bulk modulus of the formation mineral grains is K.sub.s, and formation porosity is .phi., an estimate of which can be obtained from a conventional density log.
Combining the Equations (3a) and (3b) above, with Equation (2) yields the expression: ##EQU3## However, the frame bulk modulus (K*) is still an implicit, unknown function of the formation mineralogy, porosity and rock microstructure, and the estimation of shear velocity requires some means of specifying this unknown dependence.
Previous attempts to provide appropriate values of the frame bulk modulus (K*) have relied either upon empirical correlations developed from laboratory core measurements or various simplifying ad hoc assumptions. The empirical correlations can be of the type disclosed in U.S. Pat. Nos. 4,375,090; 4,393,486; 4,398,273; and 4,399,525. Simplified ad hoc assumptions used in the past include that of K*=G* as disclosed in "Relationships Between Compressional-Wave and Shear-Wave Velocities in Elastic Silicate Rocks," Castagna et al., Geophysics (1985), 50:4, pp. 571-581.
A problem with utilizing the above methods is that laboratory core measurements representative of the subterranean formation may not be available and such ad hoc assumptions as above may be incorrect. Thus, there is a need for an alternative means of specifying dry rock bulk modulus and thereby estimating shear velocity.